Probably the Big Island. There's the Manta Night Dive, Pelagic Magic - check Jack's Diving Locker for details on both - and my buddy dove with about 200 Spinner Dolphins at a southern dive site one morning. Also you can visit Volcanoes Nat'l Park on a non-dive day. (it's at elevation) It really is the Big Island so a car would be necessary. Most of the dive boats leave from the harbor just north of Kona and many of the shops/restaurants are there also. Plus a lot of the hotels. So maybe look for something nearby. The King Kamehemaha downtown is a Courtyard by Marriott property.
The only problem you might have in October is the Ironman World Championship is there Oct 11th. So rental rates go up significantly a few weeks before to just after. And there's almost no availability anywhere - especially in Kona.
My second choice would be Kauai. It's more lush than the Big Island but there's less diving - and dive operators there. In October the best diving is likely to be blown out - Tunnels Beach and Ni'ihau. The boat operators stop going there around mid/late Sept. Need a car there also most likely, the airport is in Lihue and the diving centered around Poipu Beach - about 20? mins. south. Koloa Landing is a good shore dive and Sheraton Caverns the signature boat dive. I've done both. Dive with either Seasport Divers or Fathom Five in that area.
I haven't dove Oahu but we did go there once. Waikiki is really crowded and the better diving is elsewhere. Dive operators do pickup there - that's maybe the only place in Hawaii that they do. I liked the small Aquarium near downtown, they have something not seen elsewhere regularly (Nautilus?) We also drove out east to the more touristy aquarium - they do hookah shark dives there now IIRC. It's older and more touristy. Of course you could also see Pearl Harbor while there. Plan on traffic delays in some areas also.
Check flights, on some airlines you'll be flying thru Honolulu to get to Maui anyway. So it may be more convenient to dive there.